 Electricity and Magnetism

# Ohm's law (microscopic interpretation)

Suppose that the number of conduction electrons per unit volume in a certain metal is $n=1.23 \times 10^{29} \text{ m}^{-3}$ and the mean free time between collisions for the conduction electrons in that metal is $\tau=3.42 \times 10^{ -15} \text{ s}.$ What is the resistivity $\rho$ of that metal?

The elementary charge is $e=1.60 \times 10^{-19}\text{ C}$ and the mass of electron is $m=9.11 \times 10^{-31}\text{ kg}.$

If the number of conduction electrons per unit volume in copper is $8.47 \times 10^{28}\text{ m}^{-3}$ and the resistivity of copper is $1.61 \times 10^{-8}\,\Omega\cdot\text{m},$ what is the mean free time $\tau$ between collisions for the conduction electron in copper?

The elementary charge is $e=1.60 \times 10^{-19}\text{ C}$ and the mass of electron is $m=9.10 \times 10^{-31}\text{ kg}.$

If the mean free time between collisions for the conduction electrons in copper is $\tau=2.5 \times 10^{-14}\text{ s}$ and their effective speed $v_{\text{eff}}$ is $1.5 \times 10^6\text{ m/s},$ what is the mean free path $\lambda$ for the conduction electron in copper?

The measured resistivity of aluminium at $25\,^\circ\text{C}$ is $2.72 \times 10^{-8}\,\Omega\cdot\text{m}.$ The valency, density, and the atomic mass of aluminium are $3,$ $2.68\text{g/cm}^3,$ and $27,$ respectively. Assuming that each aluminium atom contributes three free conduction electrons to the metal, what is the mean free time between collisions for the conduction electrons in aluminium at a temperature of $25\,^\circ\text{C}?$

The elementary charge is $e=1.602 \times 10^{-19}\text{ C}.$
The mass of electron is $m=9.109 \times 10^{-31}\text{ kg}.$
The Avogadro constant is $N_A=6.022 \times 10^{23}\text{ mol}^{-1}.$

The measured electron drift mobility in silver is $57\text{ cm}^2\text{V}^{-1}\text{s}^{-1}$ at $27\,^\circ\text{C}.$ The atomic mass and density of silver are $107.87\text{ g/mol}$ and $10.70\text{ g/cm}^3,$ respectively. Assuming that each silver atom contributes one conduction electron, what is the resistivity of Ag at $27\,^\circ\text{C}?$

The elementary charge is $e=1.602 \times 10^{-19}\text{ C}.$
The mass of electron is $m=9.109 \times 10^{-31}\text{ kg}.$
The Avogadro constant is $N_A=6.022 \times 10^{23}\text{ mol}^{-1}.$

×